In terms of the leading soft graviton operator \(S_{ab}(\vec{w})\) , Weinberg's soft graviton theorem [1]}, [2]} can be written as,
\({\begin{array}{c}{\lbrace y_i,\vec{x}_i\rbrace ,out} S_{ab}(\vec{w}) {\lbrace y_j,\vec{x}_j\rbrace ,in} \nonumber = \bigg [ \sum _k \eta _k \frac{p_\mu (y_k,\vec{x}_k) p_\nu (y_k,\vec{x}_k) \epsilon ^{\mu \nu }_{ab}(\vec{w})}{p(y_k,\vec{x}_k)\cdot \hat{q}(\vec{w})}\bigg ] {\lbrace y_i,\vec{x}_i\rbrace ,out}{\lbrace y_j,\vec{x}_j\rbrace ,in}\end{array}}\) 
